Question

Which expression is the equivalent multiplication problem for 8 4/5÷4
?(1 point)

Answer 1

To convert the division expression \( 8 \frac{4}{5} \div 4 \) into an equivalent multiplication problem, you can use the fact that dividing by a number is the same as multiplying by its reciprocal.

First, convert the mixed number \( 8 \frac{4}{5} \) into an improper fraction:

1. Multiply the whole number (8) by the denominator (5): \( 8 \times 5 = 40 \).
2. Add the numerator (4): \( 40 + 4 = 44 \).
3. The improper fraction is \( \frac{44}{5} \).

Now, rewrite the division as multiplication by the reciprocal of 4:

\[
8 \frac{4}{5} \div 4 = \frac{44}{5} \div 4 = \frac{44}{5} \times \frac{1}{4}
\]

Thus, the equivalent multiplication problem is:

\[
\frac{44}{5} \times \frac{1}{4}
\]

This can also be simplified to:

\[
\frac{44 \times 1}{5 \times 4} = \frac{44}{20}
\]

So, the expression \( 8 \frac{4}{5} \div 4 \) is equivalent to \( \frac{44}{5} \times \frac{1}{4} \).